Small-scale turbulence to large-scale flows and magnetic fields: a gyrokinetic investigation
Final Report Abstract
Plasmas represent the most common state of matter in nature. Modelling their behaviour correctly is essential for understanding a large variety of natural phenomena encompassing vastly different scales ranging from astrophysical systems to laboratory experiments, that can pave the way to new ways of energy production. The main challenge to a successful quantitative description of plasmas is that they exist in a predominantly turbulent state of motion that is highly irregular and chaotic, and not well understood even in simpler settings like neutral fluids. The aim of this fellowship proposal was the study of energy transfer between different spatial scales in turbulent plasmas which, in general, lies at the core of the irregular, scaleinvariant character of turbulence. The starting point provided a fluid model known as ideal, incompressible Hall MHD that goes beyond classical magnetohydrodynamics (MHD) by taking into account the differential motion of ions and electrons in a plasma. As a result, Hall MHD possesses an additional invariant - generalized helicity - that constrains the plasma dynamics. The next step envisioned a kinetic description employing two numerical tools: GENE, a wellestablished gyrokinetic code that describes magnetized plasmas in realistic geometries, and DNA - a code based on a reduced, four-dimensional model with greater mathematical simplicity although allowing only for slab geometries. In the early stages of my project, however, it was realized that in the nearly two years after the submission of this research proposal other research groups have studied the generalized helicity as an inviscid invariant in Hall MHD and especially its effects on the generation of large-scale outflows from magnetic field energy. This, combined with recent results of my host Prof. Mahajan, pushed us into investigating the compressible Hall MHD equations. Due to the complexity of the model, a zero-pressure e approximation was developed with the aim to describe weakly-nonlinear Alfv´nic turbulence. Numerical implementations, however, revealed that essential conditions for our approximation like anisotropy (that is an important feature of magnetized plasmas and occurs in the vast majority of astrophysical settings) prevent the development of a distinctly nonlinear, turbulent regime. Another direction of research during my stay at UT Austin was focused on some fundamental turbulent characteristics in kinetic plasma systems. This was done mainly in the framework of reduced gyrokinetics with DNA but studies were later extended to full gyrokinetics and numerical simulations were also performed with GENE. That research topic was inspired by earlier works of my host Prof. Mahajan on fluid plasma models and aimed to illuminate the interplay between large-scale quantities of fundamental importance like heat/particle flux and turbulent fluctuations. Although it represented somewhat a deviation from my original research plan, this investigation focused on important issues in magnetized plasmas that are of interest to both astrophysical and tokamak research. It proved very beneficial for me during that time to be able to collaborate closely with Prof. Mahajan and Dr. Hatch (the main developer of the code DNA). Our research showed that linear characteristics like real frequency and growth rate of the largest instabilities in a magnetized plasma can predict important aspects of its nonlinear behaviour. Those findings were published in the peer-reviewed journal New Journal of Physics. During my fellowship at UT Austin I had the chance to collaborate also with Prof. Hazeltine, among others. One of his publications during that time was related to work that I have done during my studies at the Max-Planck-Institut für Plasmaphysik in Garching. It involved an approximation to the Hermite spectrum of linear plasma oscillations in a simplified setting. I managed to obtain an exact solution for that model as well as in the case of more realistic systems. Eventually, the goal is to use this exact solution to disprove the idea of linear ‘antiphase mixing’ that is sometimes quoted as an explanation why fluctuations in magnetized plasmas remain concentrated predominantly at large scales.
Publications
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Transition from week to strong turbulence in magnetized plasmas, New Journal of Physics 21, 043046 (2019)
V. Bratanov, S. Mahajan, D. R. Hatch
